Development of a qualitative reasoning model for financial forecasting
Paper type Research paper
Introduction
Qualitative reasoning systems employ model-based reasoning using qualitative values. Model-based reasoning systems are specific types of knowledge-based systems in which the underlying causal model of the system is represented. This makes the systems less brittle than heuristic systems, which fail to provide solutions outside their narrow domain of expertise (Jackson, 1990; Iwasaki and Simon, 1990). Furthermore, qualitative reasoning systems provide a mechanism for handling uncertainty by using qualitative values.
Until now, qualitative reasoning has been used mostly for physical systems (AIME, 2003; Williams et al., 2003). This has provided us with insights into the modeling principles and techniques of qualitative reasoning. However, there have been very limited applications of qualitative reasoning in business and finance (Brajnik and Lines, 1998; Apte and Hong, 1986, Hart et al., 1986). Yet, with its ability to deal with qualitative information, handling uncertainty and backtracking, qualitative reasoning can be extremely useful in business and finance domains.
The purpose of this paper is to illustrate how qualitative reasoning models can be developed in a financial domain, the applicability of these models and the problems and issues related to the development of qualitative reasoning models in finance.
Characteristics of qualitative reasoning models
To develop a qualitative reasoning model, the fundamental issues of representation, modeling principles, causality, qualitative reasoning and complexities and tasks performed will have to be dealt with (Bredeweg and Strass, 2003). These are discussed in the next section.
Representation
What characterizes a qualitative reasoning model is the how the knowledge is represented. There are two main categories of knowledge; structural and behavioral. However, even before structural and behavioral knowledge can be represented, the ontological primitives will have to be decided. Ontological primitives define the basis on which the entire knowledge structure stands. Qualitative reasoning models use different ontological primitives. For example, de Kleer and Brown (1984) take the topological structure of a device in terms of components and connections while Forbus (1996, 1990) uses the notion of physical processes. The selection of an ontological primitive over another depends on the problem on hand and the domain. The behavior of a machine can be better modeled by using components and connections while the behavior of heat flow in a volcano can be better modeled by using physical processes.
Once the ontological primitives are determined, the connections between either the components or the processes will have to be determined. These connections define the structure of the system. The structural knowledge has to be represented before reasoning can take place.
Modeling principles
Qualitative reasoning models follow some fundamental principles. The first is the locality principle (de Kleer and Brown, 1984), which states that effects can only be propagated through specified connections that are determined when the structure of the system is defined. This puts a limit on the behavioral rules that can be used, because rules that allow propagation through unspecified connections cannot be used.
The next principle is the "no function in structure" principle suggested by de Kleer and Brown (1984). According to this principle, the description of a part of a device should not assume the functioning of the whole. Basically, this principle prevents encoding the behavior of a device into the description of its components. For example, the following description is a violation of this principle: "if the switch is off no current flows and if the switch is on, current flows". This is a violation because even if a switch is on current may not flow as there may not be any potential for the current to flow (de Kleer and Brown, 1984).
Causality
Qualitative reasoning models are causal models. Simon's causal ordering offers a computational mechanism by which a causal dependency structure can be defined once the original set of equations describing the system (the structural equations) are known. Therefore the choice of structural equations is critical. Unfortunately, if there is more than one choice of the set of structural equations there are no guidelines to select the most appropriate set of structural equations. One advantage of using causal ordering is that the precise functional form of the equation need not be known. Causal ordering in an equilibrium structure is applicable to systems whose behavior is not changing with time. If the system is dynamic in nature, differential equations take the place of equilibrium structural equations. Some of the systems have a mixed structure, i.e. they are partly represented by equilibrium equations and partly by differential equations.
Causal ordering can tell us whether A causes B, but it cannot tell us whether an increase in A causes B to decrease, increase or remain the same (de Kleer and Brown, 1984). The qualitative behavior of a state can be represented by a set of equations known as confluences. In mythical causality two types of state behaviors are distinguished; the interstate behavior and the intrastate behavior. If a system is in equilibrium for an indefinite amount of time, no causal action can take place. In order to identify the existence of causality the system has to be disturbed, even if for a very short period of time. A disturbance is propagated through the system of equations by assuming a change in the value of one of the variables. This change of value is propagated through the constraint network until equilibrium is restored. If at any point sufficient local information is not available then the process stops and additional heuristics are required. This might happen when there are fewer equations than variables.
Qualitative reasoning and complexities
Since qualitative reasoning is based entirely on qualitative values, it lacks the precision offered by quantitative reasoning and can therefore lead to complexity and ambiguity. Many strategies have been used to reduce complexity and ambiguity. For example, ideological or goal-oriented knowledge can be used to develop constraints on the movement of robots, without which the movement can be in any direction.
Tasks performed
Most qualitative reasoning systems perform some type of prediction or simulation task. One common type of use is to predict the behavior of a system over time, given some initial conditions. ENVISION and QSIM represent the behavior over time as a sequence of qualitative states. In Qualitative Process Theory this is done by instances of physical objects and processes coming into existence or disappearing as a result of changes in the world.
Mathematical aspects of qualitative reasoning
The mathematics of qualitative reasoning is different from quantitative reasoning. This section explains the various approaches for resolving mathematical issues.
Representation of numbers
Three approaches have been taken to represent numbers in qualitative reasoning. These are, signs, inequalities and orders of magnitude. Signs refer to changes. If the sign of the derivative of a variable is +, then it is increasing, and if the sign is 0 it remains the same, if the sign is - then the value of the variable is decreasing. The major advantage of using signs is its simplicity (Trave-Massuyes et al., 2003, Forbus, 1996). However, signs may not be a sufficient qualitative representation for a domain. Because the sign itself might not be enough to model a domain, inequalities were added as a modeling tool. A collection of such inequalities is known as a quantity space (Forbus, 1996). If inequalities are used, the point representing boundary conditions has to be specified. These points are known as landmark values. Landmark values can be temporarily generic or specific. A temporarily generic landmark value is applicable to the system at any point in time. A temporarily specific landmark is condition specific. For example, stock market analysts may be interested in the future price of stock compared to the current price.
Inequalities might not be enough for different types of modeling. For example it might be necessary not only to know the order, but also have some idea as to how large or small the value of a variable is compared to some other variable. This gave rise to order of magnitude reasoning. Two such representations are given by the formal order of magnitude (FOG) formalism and the order of magnitude (O(M)) formalism). Since we have not used FOG or O(M), we have not discussed it any further.
Qualitative calculus
As we saw in the single equation case, the value propagation method can lead to ambiguity and render the equations unsolvable. Various strategies can be used to solve this problem. First, different value combinations can be used. This, however, leads to a combinatorial explosion (Iwasaki, 1989). The problem can be avoided using heuristic knowledge or using quantitative techniques or using a higher level of granularity extending the value propagation technique.
Other mathematical techniques have been developed with the QSIM program. The details of the QSM program and associated theoretical issues are discussed in Kuipers (1994).
Development of the qualitative reasoning model
Development of the structure
As discussed before, first the ontological primitives will have to be decided, de Kleer and Brown take the topological structure of a device in terms of components and connections while Forbus uses the notion of physical processes. Forbus' ontological primitives require the system to be represented as objects, de Kleer and Brown represent the system as a set of equations. Since financial systems are primarily represented as sets of equations, this is therefore more useful. However, the topological structure of a device is more suitable for physical systems for which it was originally intended. To get around this, the logical financial processes were used as a substitute for physical processes.
Each component essentially represented a particular aspect of the model, instead of any physical component. The structure was developed in a hierarchical fashion with net income being the component at the highest level. Figure 1 shows the first four levels of the model and how the various components interrelate.
Once the structure has been developed, the principles of qualitative reasoning were applied for further development of the model. These became constraints for model development. The locality principle states that effects can propagate only through specified connections. To follow this principle, the qualitative equations representing the system had to be developed in a fashion that connects each component to the next component without skipping any one. Referring to Figure 1 the locality principle states that net income be directly connected only to income and taxes. Therefore any change in net income will be only because there has been a change in income and/or taxes and not because of any other variables. In physical modeling, these connections are specified by the physical structure of the system.
The next principle is the "no function in structure" principle that states that the working of individual components should not assume working of the entire system. In a logical sense, therefore, if we have a partial set of equations linking only part of the structure, the system will not be valid. An entire set of equations representing the entire system is required. Only then can the forecasted value of net income be obtained.
The issue of causality and how causality has been used is more completely described when the development of the system of equations has been described in the next section.
For qualitative reasoning to be performed, the mathematical aspects of qualitative reasoning will have to be discussed. The first of this is the development of the quantity space. Signs, inequalities and orders of magnitude are the three representations of quantity spaces that can be used. In the sign representation of numbers, if the value of a variable is increasing, it can be represented by a +. K the value is decreasing, it can be represented by a - and 0 when the value remains the same. This quantity space can be used for representing increase, decrease and same for the forecast of net income. An issue in whether further granularity is required of this quantity space. Because this is a preliminary model, this simple quantity space was chosen. We do know that such simple quantity space can lead to ambiguity. The strategy to resolve ambiguity was to make use of further information.
It can be noted that most qualitative reasoning models perform some type of prediction or simulation tasks. Since the model in this case performs prediction, it can be considered to be an appropriate application.
Qualitative reasoning models are considered deep models. Depth, however, is a relative matter. In this study, the depth considered is that of a preliminary study; for applications to various corporations further depth may be necessary. However, the discussion related to the development of models shows how greater and greater depth can be achieved.
Development of the qualitative equations representing the system
The notation that follows, for representing the equations, was developed by Kuipers (1994) in which M^sup +^ represents a monotonically increasing function while M^sup -^ represents a monotonically decreasing function.
Level 1
Reasoning example and discussion
To illustrate how the system can reason using the value propagation technique, we consider two cases: one where there are no conflicts; and one where there are conflicts.
In case of no conflicts, consider the Interest module. The signs in the parentheses next to the variables provide the values while the arrows depict implications or causality. For example, Current Short Term Rate (- ) [arrow right] Short Term Interest Rate (-), should be read as, "A decrease in Current Short Term Rate causes the Short Term Interest Rate to decrease".
Many lessons can be learned from the development of this model. Unlike engineering and other physical models, there are multiple models available in finance and economics that represent the same situation. Careful model selection in that case is critical. Current research has focused on developing qualitative models through machine learning (Bratko and Suc, 2003). In most cases, these models will have a generic component that will be applicable across all organizations. It may have a component specific to a particular organization. Furthermore, selection of causal models or the ability to infer causality is necessary. While a simple qualitative representation of numbers was used, more complex qualitative representation will have to be experimented with. Since business decision making involves both qualitative and quantitative data, a procedure for integrating such information is needed for fully functional qualitative models.
Conclusions
This research shows how a qualitative reasoning model can be developed for financial systems. It shows how equations are selected, how quantitative equations are converted to qualitative equations and how reasoning takes place with such systems. Notable is the fact that this is an illustrative model and the actual model selection will depend on the situation on hand. Currently, software is being developed that can perform qualitative prediction tasks based on the model developed in this paper. Once that is done, data from various organizations will be collected for validation of the model.
References
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Further reading
Keppens, J. and Shen, Q. (2002), "On supporting dynamic constraint satisfaction with order of magnitude preferences", Proceedings of the 16th International Workshop on Qualitative Reasoning, Barcelona, pp. 75-82.
Keppens, J. and Shen, Q. (2003), "Ecological model repositories revisited: casting ecological model composition problems as dynamic constraint satisfaction problems", Proceedings of the 17th International Workshop on Qualitative Reasoning, Brasilia, August 20-22, pp. 119-29.